Hearts: Answer to question 7

Q: What is the largest losing margin? That is, what is the maximum gap between last and (perhaps equal) second last at the end of a game?

A: 122

The losing margin is greatest if the loser scores 25 on the last hand, having already scored 99, giving her a final score of 124.

The total score for all four players must be a multiple of 26. The smallest multiple of 26 which is equal to or greater than 124 is 130. The other players can share the remaining 6 points between them, scoring a total of 2 points each.

So the losing margin is 124 - 2 = 122.